Sunday, 10 July 2016

Square Dissection

I don't normally spend too much time on a single puzzle, because I have many puzzles in my collection (a lot of them Exchange Puzzles) that I have yet to go through. From my last count from two exchanges, I have still over 140 more which are untouched. I know there are those who persist with a single puzzle for weeks at an end, eg Kevin Sadler and I truly respect their efforts! But I am not one of them.

But Square Dissection got more than my usual fair share of attention because firstly I quite like packing puzzles and secondly, I also enjoy designing them and producing working copies in plexiglass for myself or for sale. So when I selected Nick Baxter's Square Dissection from my stash, which was his IPP34 Exchange Puzzle, and thinking to myself that its JUST 9 ordinary rectangles into a tray, I decided to test my solving powers on his design....and failed quite miserably!First the specs...the tray measures 9.5cm x 9.5cm x 0.6cm. The pieces are all rectangles with differing measurements for each like 18x20, 24x25 etc. These are not actual measurements but unit values of the length x width of the pieces. Both tray and pieces are made of translucent red and green acrylic/plexiglass. Everything is laser cut to perfection...and tight tolerances are indeed needed for this puzzle! The goal is to place all the 9 green rectangles into the tray with none of the pieces sticking out. Your regular 2D tray packing puzzle right? Yes, but nothing regular about it. In fact after trying for several days on and off and not getting anywhere (there is always just one last piece that refuses to go in), I did what I usually advocate; that is to ask the designer for help. Nick came back with a series of questions which were actually hints on the solve. Needless to say, these hints were lost on me and another round of email exchanges resulted in yet more hints. Still no luck and a couple of weeks later, I threw in the towel and asked for the solution. Damn...everything fits so easily and nicely into the tray! Actually there is a bit more to this puzzle that meets the eye but I shan't mention anything more here as I don't want to have any spoilers for those who may still be tearing their hair out over the Square Dissection.This puzzle may look innocuously ordinary, but there is a lot of "mathematics" behind the design and IMHO, very difficult and challenging. According to Nick, there are 23,224,320 ways to lay the pieces in a 3x3 format but only one will enable the correct fit inside the tray. And before I forget, don't waste your time with Burr Tools, it won't work.For hardcore packing fans, this is a must have! Dave Holt, hope you are reading this. Go for one!

I don't have anywhere near as many puzzles unsolved as you so I have to concentrate on the ones I have for as long as possible! After a few days I then start to play with multiple puzzles back and forth but I continue with many until I finally get them! This puzzle looks wonderful even if I am rubbish at packing puzzles.

Hmmm... I just did the math 65x65=4225 and 4225 is also the combined area of all the pieces... assuming they are labeled correctly. I may need to withdraw my comment about voids. I'm now questioning the meaning of dissection. Could you share the definition you are using?

After many attempts by hand, I typed this puzzle into BurrTools and it told me there was no solution! This led to much head scratching, were the pieces rotated? Did Nick make a mistake? Was one of the pieces cleverly mislabeled? After a few more weeks, I found the solution, but it doesn't involve any of these.

That Nick is tricky. I knew what had to be done to solve the puzzle, but without knowing the central piece, one does not have much of a chance to solve this by random means. Even a systematic method provides some 387 possibilities, but only one physical solution exists, so you'll need a checklist. I took all this talk that BT could not solve this puzzle as a challenge to overcome, and so I've used BT to successfully solve this puzzle, and it would seem that George figured out the key as well. Sorry, wwwmwww, I cannot say much more than that, without giving away too much about the key, and George's comments provide enough helpful info without giving away too much. Do re-read Jerry's blog, as he has a hint or two there as well. The arithmetic yields 4225 = 65*65, and the pieces are properly labelled... and Nick is being very clever and tricky.